In a crystal, the atoms are arranged in a periodical pattern. A box-shaped repetition unit can be formed by an imaginary connecting of several atoms. Such a box is called a unit cell. A lattice constant is a measure of the size of a unit cell, which has a dimension of length. The energies of electrons in a crystal can spread in certain ranges called energy bands. The region between adjacent energy bands is called an energy gap or a band gap. Some energy bands remain either unfilled or partially filled with electrons. Among such energy bands, the lowest one in energy is called the conduction band. Among the energy bands filled with electrons, the highest one in energy is called the valence band. Only bands that are partially, but not fully filled, contribute to electrical conduction.
Based on the structure of energy bands, crystals are usually classified in three categories: insulators, metals, and semiconductors. Metals have a conduction band that is partly empty and partly filled regardless of temperature. Insulators and semiconductors have a large (usually >4 eV) and small (<4 eV) band gap, respectively, between their conduction and valence bands.
In semiconductors at a finite temperature, electrons can be excited from the valence bands to the conduction bands by means of the thermal energy. The electron vacancies left behind in the valence bands are called holes. The number of such electrons and holes can be also controlled by intentionally doping semiconductors with impurities. When an external electric field is applied, the electrons and holes can move through the semiconductors, yielding a flow of electric current. Therefore, those electrons and holes are often called carriers. Because of various scattering mechanisms, the velocity of carriers saturates at a certain value called a drift velocity. The mobility is defined to be the magnitude of a drift velocity of carriers per unit electric field. A higher mobility can be achieved by 1) suppressing scattering events for carriers and 2) using carriers with a smaller effective mass. Carriers in a semiconductor with a smaller band gap usually have a smaller effective mass.
Crystals are components of devices which can be used in a variety of application fields, including electronics, opto-electronics, and magneto-electronics. The function of a crystalline device can often derive from a combination of crystals with different properties. Among the methods to integrate different crystals, epitaxial growth techniques are widely used because of their advantage in quality and cost. In epitaxial growth techniques, atoms are deposited on a crystalline substrate. Since the substrate acts as a template for the materials, the atoms are arranged in a crystalline form. If the grown crystal spreads over the substrate, it is called an epitaxial layer or epilayer. Depending on the growth condition and the choice of substrates, other forms of epitaxial crystals can be obtained. Epitaxial dots and wires are representatives of such crystals. An epitaxially grown crystal can act as a substrate for another epitaxial growth.
The lattice constant of a material is a temperature-dependent intrinsic property of the bulk form of that material. If an epitaxially grown crystal has a lattice constant different than the substrate, the difference between the two constants yields a lattice mismatch. A lattice mismatch, f, is usually defined to be f=[LCsub−LCepi]/LCepi×100(%), where LCsub and LCepi are intrinsic lattice constants of the substrate and the epitaxially grown crystal, respectively. For an epitaxial growth with f≠0%, the stress in an epitaxially grown crystal which strongly depends on the magnitude of f becomes larger as the thickness increases. When the thickness is small, the stress can be resolved by elastically deforming the unit cell of the epitaxially grown crystal, which results in the epitaxially grown crystal being strained. When the thickness becomes larger, the stress can reach a point where structural defects, such as dislocations and cracks, are created and elongated in the epitaxially grown crystal. The thickness at which this phenomenon occurs is usually called a critical thickness. Although a crystal can be grown epitaxially beyond a critical thickness in most of the cases, the quality of the epitaxial crystal is largely deteriorated due to structural defects. Structural defects can limit the performance of crystalline devices which use epitaxially grown crystals.
An example of an ordinary epitaxial growth is presented in FIG. 1. For simplicity, only the case for an epitaxial layer is shown. Layer 2 is epitaxially grown on a substrate, layer 1. Layer 1 can be either a thick continuous crystal or a crystal grown epitaxially on another crystal. In either case, the deformation of layer 1 is negligible. Therefore, the lattice mismatch between layer 1 and layer 2 can be calculated by using the intrinsic lattice constants for these layers. The thinner solid curve in FIG. 6 shows a typical critical thickness curve plotted as a function of lattice mismatch. The shape of curve can be altered depending on other parameters, such as the mechanical properties of layer 1, the types of structural defects, and the condition of epitaxial growth. FIG. 6 indicates that if layer 2 is an active (main) layer of a device, its thickness is effectively limited by the critical thickness. Beyond the critical thickness, structural defects that can lower the device performance are created. The critical thickness becomes smaller as the lattice mismatch increases.
It is often the case that the optimum epitaxial crystal thickness for device performance is thicker than the critical thickness for a given material combination. Moreover, the pursuit of improved device performance often dictates the use of new material combinations with a larger lattice mismatch, because this usually coincides with a desirable relationship in the difference of other material properties, such as band-gap. A larger lattice mismatch, however, incurs an even smaller critical thickness for the layered structures, as shown in FIG. 6. The presently disclosed and claimed invention can overcome the ordinary critical thickness limitation for structures used in a variety of applications. The thicker solid curve in FIG. 6 shows a possible shift in the critical thickness curve by the presently disclosed and claimed invention. Usually, the critical thickness is increased for the entire lattice mismatch range.